They claim they can't work any more, unless they get this one piece of crucial information from you. And your boss must ensure that you reply to them, when they need to. Ultimately, if done cleverly enough, you will look like a bad employee long term, unless you give in.
Again, tools can help modulate the above behavior and even build norms. But ultimately, they only work if everyone agrees to the same set of social norms.
Enforcing said appropriate social norms is a big part of the reason there is management in the first place. However it means that
1) Management has to be technically competent enough to understand the things being communicated about.
2) Management has to be motivated to enforce appropriate social norms.
These are both pretty difficult to achieve in practice.
I feel this is a key thing that makes chat work really well for some remote workers and terribly for others: what's the expectation of responsiveness to chat?
For example, if you feel you need to respond to any DM (either implicitly due to company culture or explicitly because your boss has brought it up as a complaint about you), then slack is a huge interruption. You probably feel the need to have intrusive notifications enabled and/or a bouncing dock icon indicating new messages.
On the other hand, if the norm at your company is "slack is async so expect a response in 2-3 business hours," then yeah - it's rarely, if ever, interrupting.
Again, tools can help modulate the above behavior and even build norms. But ultimately, they only work if everyone agrees to the same set of social norms.